Recovering information about a finite group from its subrack lattice
JOURNAL OF ALGEBRA, vol.582, pp.26-38, 2021 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 582
- Publication Date: 2021
- Doi Number: 10.1016/j.jalgebra.2021.04.026
- Journal Name: JOURNAL OF ALGEBRA
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
- Page Numbers: pp.26-38
- Keywords: Subrack lattice of a group, Nilpotence class, p-Nilpotence
- Middle East Technical University Affiliated: No
Abstract
We prove that the isomorphism type of the subrack lattice of a finite group determines the nilpotence class. We analyze the problem of estimating the orders of the group elements corresponding to the atoms of the subrack lattice. As a result, we show that the subrack lattice determines p-nilpotence of the group if a certain condition is met. (C) 2021 Elsevier Inc. All rights reserved.